CN108845576B - Thrust distribution method based on combination of particle swarm optimization and sequence quadratic programming - Google Patents
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Abstract
The invention relates to a thrust distribution method based on the combination of particle swarm optimization and sequential quadratic programming, which is technically characterized in that: the method comprises the following steps: step 1, a thrust distribution unit obtains a current controller triaxial instruction from a controller, wherein the current controller triaxial instruction comprises a longitudinal force, a transverse force and a yawing moment; step 2, establishing a thrust distribution model of the dynamic positioning system; step 3, establishing a target function and a constraint condition of the thrust distribution problem; and 4, solving the thrust distribution problem by using an optimization method combining particle swarm optimization and sequential quadratic programming. The method combines the advantages and the disadvantages of the particle swarm algorithm and the sequence quadratic programming algorithm on the basis of fully considering the advantages and the disadvantages of the particle swarm algorithm and the sequence quadratic programming algorithm, so that the disadvantages of the particle swarm algorithm and the sequence quadratic programming algorithm can be effectively compensated, the global optimization performance of the algorithm is greatly improved, the thrust distribution problem of a dynamic positioning system can be quickly and effectively solved, and the method has high practical value.
Description
Technical Field
The invention belongs to the technical field of ship dynamic positioning, relates to a thrust distribution method of a ship dynamic positioning system, and particularly relates to a thrust distribution method based on the combination of particle swarm optimization and sequence quadratic programming.
Background
With the continuous development of the ocean by human beings, the traditional anchoring and positioning system cannot meet the operation requirement of deep sea water areas. The dynamic positioning system can resist the interference of the marine environment by using the propeller of the ship, realizes the maintenance of the position and the heading of the ship, has the advantages of high positioning precision, strong maneuverability, no limitation of the depth of the sea area and the like, and is one of necessary guarantee equipment of deep sea operation equipment.
The thrust distribution task of the ship dynamic positioning system is to reasonably distribute three-degree-of-freedom control instructions output by a dynamic positioning controller to each propeller according to a certain distribution strategy so as to output expected resultant force and moment. At present, a ship is generally provided with a plurality of propellers, so that countless solutions exist on the premise of meeting control instructions. The thrust distribution problem can be summarized as a nonlinear optimization problem under the condition of considering factors such as energy consumption of the thruster, wear of the thruster, thrust error and the like.
Through search, the thrust distribution is realized by applying a particle swarm algorithm in the patent application with the publication number of CN102508431A and the name of 'a thrust distribution method of a dynamic positioning system of an offshore drilling platform'. In patent application CN106773741A entitled "a system and method for positioning unmanned ship dynamically", thrust allocation is realized by using a particle swarm algorithm with improved inertia factors, which is an improved particle swarm algorithm. In the optimization process of a single particle swarm algorithm, the randomness is particularly high, the optimization result of each time fluctuates near an optimal value, so that the thrust distribution result generated by the particle swarm algorithm has particularly high variation frequency of the thrust and the azimuth of each thruster, even if the thrust distribution result is the same control instruction, the thruster instruction generated each time is different, the control on the thruster is very unfavorable, the wear of the thruster is aggravated by the frequent action of the thruster, and the service life of the thruster is shortened.
In patent publication CN103092077A entitled "thrust allocation method for dynamic positioning system", thrust allocation is implemented by using a sequential quadratic programming algorithm. However, the dependence of the sequential quadratic programming algorithm on the initial value is particularly large, and the phenomenon that the optimal solution cannot be found due to improper selection of the initial value may be caused.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a thrust distribution method based on the combination of particle swarm optimization and sequence quadratic programming, which is reasonable in design, rapid, effective and strong in global optimization performance.
A thrust distribution method based on the combination of particle swarm optimization and sequential quadratic programming comprises the following steps:
step 3, establishing a target function and a constraint condition of the thrust distribution problem;
step 4, solving the thrust distribution problem by using an optimization method combining particle swarm optimization and sequential quadratic programming;
furthermore, the mathematical description of the dynamic positioning system thrust distribution model of step 2 is as follows:
τ＝(X,Y,N)T＝B(α)T
wherein T ═ T (T)1,T2…Tn)TRepresenting the thrust magnitude of n propellers;
α＝(α1,α2…αn) Representing the azimuth angles of the n thrusters;
in the above formula, (l)xi,lyi) Indicating the position of the ith propeller relative to the center of rotation of the vessel.
Moreover, the objective function of the thrust force distribution problem of step 3 includes: executing energy consumption, thrust error of a control system and a propulsion system and propeller abrasion; the mathematical description is as follows:
j (α, T) represents an objective function of the thrust allocation problem, and the above expression means that the objective function value is minimized by selecting different α and T. It is composed ofThe middle α and T represent the azimuth and thrust magnitude of the propeller, respectively. In the above formula, the first and second carbon atoms are,
w is a weight matrix for energy consumption of all the actuating mechanisms; sTQS represents three-degree-of-freedom thrust error, Q is a positive fixed diagonal matrix, and S ═ τ -B (α) T is a relaxation variable; (alpha-alpha)0)TΩ(α-α0) For propeller wear, Ω is also a positive definite matrix, α0The azimuth angle of each propeller at the last moment;
furthermore, the constraint conditions of the objective function of the thrust force distribution problem in step 3 are as follows:
in the above formula, T and alpha represent the thrust and azimuth angle of the propeller at the present moment, T0And alpha0Representing the thrust and azimuth of the propeller, Δ T, at the previous momentmin,ΔTmax,Δαmin,ΔαmaxRespectively representing the minimum and maximum variation ranges of the thrust and the azimuth of the propeller;
further, the specific steps of step 4 include:
(1) initializing particle swarm algorithm parameters: setting a population scale N, a dimension D of a solution and a maximum iteration number T;
(2) randomly initializing the speed and position of the population: the velocity of each particle represents the varying velocity of the thrust and azimuth of the respective propeller; the position vector of each particle represents a vector consisting of the thrust and azimuth of the respective propeller;
(3) calculating an objective function value according to the position information of each particle, and updating a historical optimal function value and a group optimal function value of each particle;
(4) updating the state of the particle according to a velocity and position updating formula of the particle, wherein the velocity and position updating formula of the particle is as follows:
in the above formula, i is 1,2, …, m represents the number of populations, D is 1,2, …, D represents the dimension of the problem to be solved, and the state of each particle contains position information xi(t)＝[xi1(t),xi2(t),…xiD(t)]And velocity vector information vi(t)＝[vi1(t),vi2(t),…viD(t)](ii) a Each particle can record the historical optimal position p once found by itselfi(t)＝[pi1(t),pi2(t),…piD(t)]Meanwhile, the position information p of the globally optimal particle in the group can be shared among the particlesg(t)＝[pg1(t),pg2(t),…pgD(t)](ii) a Acceleration constant c1And c2Is a non-negative constant, r1And r2Is from [0,1 ]]A random number of (c); and when
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
and
representing the minimum and maximum velocities of the particle flight;
(5) and (3) comparing the fitness of each particle: solving the fitness of each particle, namely an objective function value, finding out the particle with the highest fitness in the population, and comparing each fitness with the value of the previous moment to obtain the highest fitness of the particle;
(6) and (5) repeating the step (3) to the step (5) until the maximum iteration times is reached, and obtaining the optimal distribution result found by the particle swarm algorithm.
(7) And taking the optimal distribution result obtained by the particle swarm optimization as an initial value, and solving by using a sequence quadratic programming method.
(8) And outputting the optimal distribution result searched by the sequential quadratic programming algorithm, namely the output thrust and the direction of each thruster.
The invention has the advantages and beneficial effects that:
1. the invention discloses a thrust distribution method of a dynamic positioning system based on the combination of particle swarm and sequential quadratic programming, which is characterized in that the goals of minimum energy consumption and minimum abrasion of all executing mechanisms are realized on the basis of meeting the control instructions of three degrees of freedom on the horizontal plane of the dynamic positioning system, namely surging, swaying and yawing respectively. The method comprises the following steps: firstly, giving three-degree-of-freedom control instructions of longitudinal force, transverse force and yawing moment; secondly, establishing a thrust distribution nonlinear mathematical model: and the constraint conditions take the energy consumption, the abrasion and the thrust error of all the actuating mechanisms as the minimum objective function and take the factors of thrust, the azimuth angle change rate, a thrust forbidden zone and the like into consideration. And finally, solving the thrust distribution problem by using a method of combining particle swarm optimization and sequential quadratic programming to obtain the azimuth angle instruction of each actuating mechanism. The method combines the advantages and the disadvantages of the particle swarm algorithm and the sequence quadratic programming algorithm on the basis of fully considering the advantages and the disadvantages of the particle swarm algorithm and the sequence quadratic programming algorithm, so that the disadvantages of the particle swarm algorithm and the sequence quadratic programming algorithm can be effectively compensated, the global optimization performance of the algorithm is greatly improved, the thrust distribution problem of a dynamic positioning system can be quickly and effectively solved, and the method has high practical value.
2. Aiming at the defects of the single particle swarm algorithm and the single sequence quadratic programming algorithm, the invention fuses the single particle swarm algorithm and the single sequence quadratic programming algorithm, and overcomes the defect of overhigh change frequency of an output result caused by the randomness of the single particle swarm algorithm; meanwhile, the output result of the particle swarm optimization is used as the initial value of the sequence quadratic programming algorithm, and the defect that the single sequence quadratic programming algorithm has large degree of dependence on the initial value is overcome. The optimization precision of the fusion algorithm is high, and the engineering practicability is strong.
3. The particle swarm optimization method has the advantages that an initial value is given, so that particularly high precision is not required, a large amount of time is not required to be consumed for iteration on the premise of meeting the optimization precision, the calculation time can be greatly reduced, and the real-time requirement of a dynamic positioning system is met.
4. The fusion algorithm based on the combination of the particle swarm and the sequence quadratic programming has very low requirements on the setting of the form and the initial value of the objective function, simple algorithm parameters, convenient adjustment and high algorithm optimization precision, and can quickly and effectively solve the problem of thrust distribution.
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FIG. 1 is a process flow diagram of the present invention;
FIG. 2 is a block diagram of the dynamic positioning system of the present invention;
fig. 3 is a propeller layout.
Detailed Description
The embodiments of the invention will be described in further detail below with reference to the accompanying drawings:
a thrust allocation method based on the combination of particle swarm optimization and sequential quadratic programming is disclosed, as shown in FIG. 1, and comprises the following steps:
τ＝(X,Y,N)T＝B(α)T
wherein T ═ T (T)1,T2…Tn)TRepresenting the thrust magnitude of n propellers;
α＝(α1,α2…αn) Representing the azimuth angles of the n thrusters;
(lxi,lyi) Indicates the ith pushThe position of the propeller relative to the centre of rotation of the vessel;
step 3, establishing a target function and a constraint condition of the thrust distribution problem;
the objective function of the thrust force distribution problem of step 3 comprises: executing energy consumption, thrust error of a control system and a propulsion system and propeller abrasion; the mathematical description is as follows:
j (α, T) represents an objective function of the thrust allocation problem, and the above expression means that the objective function value is minimized by selecting different α and T. Where α and T represent the azimuth and thrust magnitude of the propeller, respectively. In the above formula, the first and second carbon atoms are,
w is a weight matrix for energy consumption of all the actuating mechanisms; sTQS represents three-degree-of-freedom thrust error, Q is a positive fixed diagonal matrix, and S ═ τ -B (α) T is a relaxation variable; (alpha-alpha)0)TΩ(α-α0) For propeller wear, Ω is also a positive definite matrix, α0The azimuth angle of each propeller at the last moment;
in this embodiment, the specific values are:
W＝[60606060]，Q＝diag[1500080000100000]，Ω＝diag[400000400000]。
the constraint conditions of the objective function of the thrust allocation problem in the step 3 are as follows:
the thrust distribution problem constraint condition needs to consider the actual physical limitations of the propeller besides the requirement of the force balance equation, including the thrust size and change limitation, the azimuth size and change limitation, and the like, and the mathematical description is as follows:
in the above formula, T and alpha represent the thrust of the propeller at the present moment andazimuth, T0And alpha0Representing the thrust and azimuth of the propeller, Δ T, at the previous momentmin,ΔTmax,Δαmin,ΔαmaxRespectively representing the minimum and maximum variation ranges of the thrust and the azimuth of the propeller;
in the present embodiment, T1max＝T2max＝300KN，T1min＝T2min＝0KN；T3max＝T3max＝420KN，T3min＝T3min＝-285KN；α1max＝α2max＝360°，α1min＝α2min＝0°，α3＝α4＝90°；ΔT1max＝ΔT2max＝18KN，ΔT1min＝ΔT2min＝0KN，ΔT3max＝ΔT4max＝25KN，ΔT3min＝ΔT4min＝0KN；Δα1max＝Δα2max＝10°，Δα1min＝Δα2min＝0°。
Step 4, solving the thrust distribution problem by using an optimization method combining particle swarm optimization and sequential quadratic programming;
the specific steps of the step 4 comprise:
(1) initializing particle swarm algorithm parameters: setting a population scale (the number of candidate solutions) N, a dimension D of the solution and a maximum iteration number T;
in this embodiment, the particle swarm algorithm is not required to obtain a very accurate solution, and only an approximate range of the optimal solution is required to be obtained, so that the population number and the iteration number can be correspondingly set to be smaller, so as to increase the calculation speed of the algorithm. Therefore, in the invention, the population number N is 10, the dimension D of the solution is 6, and the maximum iteration number T is 50.
(2) Randomly initializing the speed and position of the population: the velocity of each particle represents the varying velocity of the thrust and azimuth of the respective propeller; the position vector of each particle represents a vector consisting of the thrust and azimuth of the respective propeller;
(3) calculating an objective function value according to the position information of each particle, and updating a historical optimal function value and a group optimal function value of each particle;
(4) updating the state of the particle according to a velocity and position updating formula of the particle, wherein the velocity and position updating formula of the particle is as follows:
in the above formula, i is 1,2, …, m represents the number of populations, D is 1,2, …, D represents the dimension of the problem to be solved, and the state of each particle contains position information xi(t)＝[xi1(t),xi2(t),…xiD(t)]And velocity vector information vi(t)＝[vi1(t),vi2(t),…viD(t)](ii) a Each particle can record the historical optimal position p once found by itselfi(t)＝[pi1(t),pi2(t),…piD(t)]Meanwhile, the position information p of the globally optimal particle in the group can be shared among the particlesg(t)＝[pg1(t),pg2(t),…pgD(t)](ii) a Acceleration constant c1And c2Is a non-negative constant, r1And r2Is from [0,1 ]]A random number of (c); and when
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
and
representing the minimum and maximum velocities of the particle flight;
in this embodiment, an acceleration constant is takenc10.4 and c20.6 is a non-negative constant;
(5) and (3) comparing the fitness of each particle: solving the fitness of each particle, namely an objective function value, finding out the particle with the highest fitness in the population, and comparing each fitness with the value of the previous moment to obtain the highest fitness of the particle;
(6) and (5) repeating the step (3) to the step (5) until the maximum iteration times is reached, and obtaining the optimal distribution result found by the particle swarm algorithm.
(7) And taking the optimal distribution result obtained by the particle swarm optimization as an initial value, and solving by using a sequence quadratic programming method.
(8) And outputting the optimal distribution result searched by the sequential quadratic programming algorithm, namely the output thrust and the direction of each thruster.
The dynamic positioning system of the invention is shown in fig. 2 and mainly comprises a measuring system, a propeller system, a control system and the like.
(1) The measuring system carries out signal processing on the measured ship state data (including position, heading and attitude information) to improve the accuracy of signals, wherein the signal processing comprises processing of a wild value, time, space alignment and the like. And transmitting the processed signal to a state observer, generally filtering the processed measurement information in an extended Kalman filtering manner for feedback control, and effectively filtering noise in the measurement signal by the extended Kalman filtering technology to reduce the abrasion and energy consumption of the propeller.
(2) The control system mainly calculates the control force (moment) of three degrees of freedom of a ship horizontal plane required for keeping or changing the position/heading of the ship, and mainly comprises deviation feedback and wind feedforward; wherein, the deviation feedback is to calculate the deviation feedback force (moment) needed to maintain or change the position/heading of the ship by using the deviation between the state of the ship position, heading, speed, rotation angular speed and the like output from the measuring system and the position/heading set value. Wind feedforward is to calculate wind load according to a ship wind power model by utilizing wind speed and wind direction measured values measured by a wind sensor. The wind load feedforward control force (moment) is equal to the wind load in magnitude and opposite in direction.
The control system finally outputs the control force of three degrees of freedom (longitudinal, transverse and heading) of the horizontal plane required by the ship for keeping or changing the position/heading, the control force is transmitted to the thrust distribution unit, the three-axis control force is converted into the control instruction of each actuating mechanism through thrust distribution, and the aim of keeping or changing the position/heading of the ship is fulfilled through the action of the propeller.
As shown in fig. 3, the propeller configuration of the controlled object according to the present invention can be seen, wherein the # 1 propeller and the # 2 propeller are all-rotation propellers; the No. 3 and No. 4 propellers are channel propellers. In which the position of each propeller (l)xi,lyi) Respectively as follows: 1# propeller (-34.5, -12.0); 2# propeller (-34.5, 12.0); 3# propeller (22.0, 0); 4# propeller (28.4, 0).
The working principle of the invention is as follows:
the actual position and the heading of the ship are obtained through a ship state observer and are compared with the set position and the heading, the deviation of the actual position and the heading is transmitted to a controller, the controller outputs a required three-degree-of-freedom control instruction, and the control instruction of each actuating mechanism is obtained through thrust distribution so as to counteract the action of the external environment. The invention mainly relates to a thrust distribution optimization method, namely how to change a control command output by a controller into a control command of each actuating mechanism.
It should be emphasized that the examples described herein are illustrative and not restrictive, and thus the present invention includes, but is not limited to, those examples described in this detailed description, as well as other embodiments that can be derived from the teachings of the present invention by those skilled in the art and that are within the scope of the present invention.
Claims (4)
1. A thrust distribution method based on the combination of particle swarm optimization and sequential quadratic programming is characterized in that: the method comprises the following steps:
step 1, a thrust distribution unit obtains a current controller triaxial instruction from a controller, wherein the current controller triaxial instruction comprises a longitudinal force, a transverse force and a yawing moment;
step 2, establishing a thrust distribution model of the dynamic positioning system;
step 3, establishing a target function and a constraint condition of the thrust distribution problem;
step 4, solving the thrust distribution problem by using an optimization method combining particle swarm optimization and sequential quadratic programming;
the specific steps of the step 4 comprise:
(1) initializing particle swarm algorithm parameters: setting a population scale N, a dimension D of a solution and a maximum iteration number T;
(2) randomly initializing the speed and position of the population: the velocity of each particle represents the varying velocity of the thrust and azimuth of the respective propeller; the position vector of each particle represents a vector consisting of the thrust and azimuth of the respective propeller;
(3) calculating an objective function value according to the position information of each particle, and updating a historical optimal function value and a group optimal function value of each particle;
(4) updating the state of the particle according to a velocity and position updating formula of the particle, wherein the velocity and position updating formula of the particle is as follows:
in the above formula, i is 1,2, …, m represents the number of populations, D is 1,2, …, D represents the dimension of the problem to be solved, and the state of each particle contains position information xi(t)＝[xi1(t),xi2(t),…xiD(t)]And velocity vector information vi(t)＝[vi1(t),vi2(t),…viD(t)](ii) a Each particle can record the historical optimal position p once found by itselfi(t)＝[pi1(t),pi2(t),…piD(t)]Meanwhile, the position information p of the globally optimal particle in the group can be shared among the particlesg(t)＝[pg1(t),pg2(t),…pgD(t)](ii) a Acceleration constant c1And c2Is a non-negative constant, r1And r2Is from [0,1 ]]A random number of (c); and when
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
and
representing the minimum and maximum velocities of the particle flight;
(5) and (3) comparing the fitness of each particle: solving the fitness of each particle, namely an objective function value, finding out the particle with the highest fitness in the population, and comparing each fitness with the value of the previous moment to obtain the highest fitness of the particle;
(6) repeating the step (3) to the step (5) until the maximum iteration times is reached, and obtaining the optimal distribution result found by the particle swarm algorithm;
(7) taking the optimal distribution result obtained by the particle swarm optimization as an initial value, and solving by using a sequence quadratic programming method;
(8) outputting the optimal distribution result searched by the sequential quadratic programming algorithm, namely the output thrust and the direction of each thruster;
the feasible region of the full-rotation propeller is defined as follows: t is1max＝T2max＝300KN，T1min＝T2min＝0KN；α1max＝α2max＝360°，α1min＝α2min＝0°。
2. The thrust based on the combination of particle swarm and sequential quadratic programming according to claim 1An allocation method, characterized by: the mathematical description of the thrust distribution model of the dynamic positioning system in the step 2 is as follows: τ ═ (X, Y, N)T＝B(α)T
Wherein T ═ T (T)1,T2…Tn)TRepresenting the thrust magnitude of n propellers;
α＝(α1,α2…αn) Representing the azimuth angles of the n thrusters;
in the above formula, (l)xi,lyi) Indicating the position of the ith propeller relative to the center of rotation of the vessel.
3. The thrust allocation method based on the combination of the particle swarm and the sequential quadratic programming according to claim 1, characterized in that: the objective function of the thrust force distribution problem of step 3 comprises: executing energy consumption, thrust error of a control system and a propulsion system and propeller abrasion; the mathematical description is as follows:
j (alpha, T) represents an objective function of the thrust distribution problem, and the expression means that the objective function value is minimized by selecting different alpha and T; wherein α and T represent the azimuth and thrust magnitude of the propeller, respectively; in the above formula, the first and second carbon atoms are,
w is a weight matrix for energy consumption of all the actuating mechanisms; sTQS represents three-degree-of-freedom thrust error, Q is a positive fixed diagonal matrix, and S ═ τ -B (α) T is a relaxation variable; (alpha-alpha)0)TΩ(α-α0) For propeller wear, Ω is also a positive definite matrix, α0The azimuth angle of each propeller at the previous moment.
4. The thrust allocation method based on the combination of the particle swarm and the sequential quadratic programming according to claim 1, characterized in that: the constraint conditions of the objective function of the thrust allocation problem in the step 3 are as follows:
in the above formula, T and alpha represent the thrust and azimuth angle of the propeller at the present moment, T0And alpha0Representing the thrust and azimuth of the propeller, Δ T, at the previous momentmin,ΔTmax,Δαmin,ΔαmaxRepresenting the minimum and maximum variation ranges of thrust and azimuth of the propeller, respectively.
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